This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously. Instead of using two tuning parameters, the proposed iterative algorithm enables only one optimal tuning parameter in each step and is more efficient. The authors establish asymptotic normality for the proposed estimators of quantile regression coefficients. Simulation studies show that the new method is robust to a variety of error distributions at different quantiles. It outperforms the traditional regression models under a wide array of simulated data models and is flexible enough to accommodate changes in fixed and random effects. For the high dimensional data scenarios, the new method still can correctly select important variables and exclude noise variables with high probability. A case study based on a hierarchical education data illustrates a practical utility of the proposed approach.

提出了线性混合效应模型的双重惩罚分位数回归，可以同时选择固定效应和随机效应。代替使用两个调整参数，所提出的迭代算法在每个步骤中仅启用一个最佳调整参数，并且效率更高。作者建立了分位数回归系数的估计量的渐近正态性。仿真研究表明，该新方法对于不同分位数下的各种误差分布具有鲁棒性。在大量的模拟数据模型下，它的性能优于传统的回归模型，并且足够灵活，可以适应固定效应和随机效应的变化。对于高维数据场景，新方法仍然可以正确选择重要变量，并以较高的概率排除噪声变量。